CHAPTER I Sets, Functions, and Integers
CHAPTER II Groups
CHAPTER III Rings
CHAPTER IV Universal Constructions
CHAPTER V Modules
CHAPTER VI Vector Spaces
CHAPTER VII Matrices
CHAPTER VIII Special Fields
CHAPTER IX Determinants and Tensor Products
CHAPTER X Bilinear and Quadratic Forms
CHAPTER XI Similar Matrices and Finite Abelian Groups
CHAPTER XII Structure of Groups
CHAPTER XIII Galois Theory
CHAPTER XIV Lattices
CHAPTER XV Categories and Adjoint Functors
CHAPTER XVI Multilinear Algebra

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance.

This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach—emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s—was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors. --- summary provided by publisher